Question

the radian measure of a interior angle of regular polyhon of 12 side is

Answer 1

The total interior angle of a 12 sided polygon is = (12 - 2) 180 degrees = 1800 degrees. The internal angle at each vertex of an regular dodecagon is equal to = = 150 degrees. While the exterior angle at a single vertex is = = 30 degrees. The total exterior angle of a 12 sided polygon is 360 degrees.

Answer 2

In any polygon sum of all the interior angles is given by 180(n−2) where n is the number of sides of the polygon and each angle of a regular polygon is given by 180(n−2)n

measure of ext angle = 180 - int angle

interior angle of a regular polygon is given by 180(n−2)n

=> measure of ext angle =180−180(n−2)n

=180n−180n+360n

=360n

n = 12

=> each ext angle =30